FINDING THE COMPLIMENT OF A GRAPH Jeffrey Martinez

FINDING THE COMPLIMENT OF A GRAPH Jeffrey Martinez Math 170 Dr. Lipika Deka 12/19/13

Chapter 10. 1 Problem #39

Compliment of a Graph • From our text, we find the definition of “The Compliment” of a graph: • Definition: If G is a simple graph, the complement of G, denoted G′, is obtained as follows: The vertex set of G′ is identical to the vertex set of G. However, two distinct vertices v and w of G′ are connected by an edge if, and only if, v and w are not connected by an edge in G.

Problem #39 part (a) • The Graph of G in part (a) is shown with vertexes from v 1 to v 2, from v 1 to v 4, from v 2 to v 3, and from v 2 to v 4. • To find the compliment G’, we keep the vertexes the same, but instead connect any vertexes that did not have an edge between them in G. In this case it is from v 1 to v 3, and from v 3 to v 4. A rough sketch of G’ is shown below. v 2 v 3 v 1 v 4

Problem #39 part (b) • The Graph of G in part (b) is shown with vertexes from v 1 to v 2, and from v 3 to v 4. • Once again, like part (a), to find the compliment G’, we keep the vertexes, connecting any vertexes that do not have an edge between them in the graph of G. In this case it is from v 1 to v 3, from v 1 to v 4, from v 2 to v 4 and from v 2 to v 3. A rough sketch of G’ is shown below. v 2 v 1 v 3 v 4